Module 
Date 
Topic 
Notes 
1: Probability Basics I

01/18 
Sample space, Events, Axioms of probability 
BT Chap. 1.11.2 
01/23 
Sets, Probability Laws 
BT Chap. 1.11.2 
2: Counting/Combinatorics

01/25 
Counting Rules, Permutations, Combinations 
BT 1.6 
01/30 
Repetitions, Objects into Boxes 
BT 1.6 
02/01 
Counting and Probability 
BT 1.6 
3: Probability Basics II

02/06 
Conditional Probability, Multiplication rule 
BT 1.3 
02/08 
Total Probability Theorem, Bayes Rule 
BT 1.4 
02/13 
Independence: Given two events, Conditional independence 
BT 1.5 
02/15 
Independence: Given a collection of events, Pairwise Independence 
BT 1.5 
4: Discrete Random Variables

02/20 
Discrete Random Variables, Probability Mass Function (PMF), Functions of Random Variables 
BT 2.12.3 
02/22 
Expectation, Variance, Conditional PMF (given event), Cond. Expectation 
BT 2.4 
02/27 
Total Expectation Theorem, Joint PMF, Conditional PMF 
BT 2.5, 2.6 
02/29 
Independent Random Variables 
BT 2.5, 2.7 
03/05 
Review 
BT Chap. 1, 2 
03/07 
Midterm 
BT Chap. 1, 2 
03/12 
Spring Break 

03/14 
Spring Break 

5: Continuous Random Variables

03/19 
Continuous Random Variables, Probability distribution function, Cumulative distribution functions, Normal Random Variables 
BT 3.13.3 
03/21 
Multiple Random Variables: Joint PDFs, Conditioning, Independence 
BT 3.43.5 
03/26 
Conditional PDF, Continuous Bayes Rule 
BT 3.53.6 
03/28 
Review 

6: Advanced Probability

04/02 
Covariance, Correlation, Conditional Expectation 
BT 4.24.3 
04/04 
Conditional Expectation and Variance Contd. 
BT 4.3 
04/09 
Sum of Random Number of Random Variables, Transforms 
BT 4.44.5 
6: Bayesian Statistical Inference

04/11 
Intro to Statistics, Bayesian Inference

BT 8.1 
04/16 
MAP Rule, Conditional Expectation Estimator 
BT 8.28.3 
7: Classical Statistical Inference

04/18 
Maximum Likelihood Estimation, Desirable Properties of Estimators 
BT 9.1 
04/23 
Estimating the mean and variance of a random variable, Confidence Intervals 
BT 9.1 
04/25 
Hypothesis Testing 
BT 9.3 
04/30 
Review of Statistics 

05/02 
Review of Probability 
